Question

Find the first four terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.an = 4(3)n

Answer 1

`12,36,108,324`

1) Since we've been told the Explicit Formula for this Geometric Sequence, then we can find the first four terms, namely:

`a_1,a_2,a_3,a_4`

2) Thus, plugging into each term n=1, n=2,n=3,n=4 we've got the following below:

`\begin{gathered} a_1=4(3)^1=12 \\ a_2=4(3)^2=36 \\ a_3=4(3)^3=108 \\ a_4=4(3)^4=324 \end{gathered}`

Note that each term is thrice the previous one. And that is the answer.